CFD modeling of a bounded domain with viscous region partitioning

Abstract

A hybrid computational fluid dynamics (CFD) approach is provided for modeling a bounded domain by processing the domain to automatically locate a viscous region(s) by: dividing the domain into cells and determining flow characteristic values for cells; defining characteristic cutoff values using multiple cutoff percentiles of cells and the flow characteristic values, and defining ranges between cutoff values, and respective χ values, where one χ value is a highest χ value R; assigning χ values to cells based on the determined flow characteristic values in comparison to the cutoffs; selectively increasing the assigned χ value of a cell(s) sharing a border with a seed cell having χ value R; identifying a viscous region where multiple contiguous cells have assigned χ values equal or above a threshold; evaluating the viscous region(s) by performing viscous domain solve; and providing a model of the domain using results of the viscous domain solve.

What is claimed is: 
     
       1. A data center comprising:
 an air-conditioning unit, and one or more electronics racks; and 
 a computer system comprising:
 a memory; and 
 a processor in communications with the memory, wherein the computer system performs a method, the method comprising:
 providing a data center layout optimized for data center energy efficiency, the data center being a bounded domain and the providing comprising:
 performing computational fluid dynamics modeling of the bounded domain, the performing comprising: 
  processing the bounded domain to automatically locate within the bounded domain at least one viscous region of the bounded domain, the processing comprising: 
  dividing the bounded domain into a plurality of cells, and determining a flow characteristic value for cells of the plurality of cells of the bounded domain; 
  defining turbulence characteristic cutoff values using, at least in part, multiple cutoff percentiles of cells and the determined flow characteristic values, and defining ranges between the defined characteristic cutoff values with respective χ values, one respective χ value being a highest χ value ‘R’, where ‘R’ is a selected viscous region cell radius; 
  assigning, using the respective χ values of the ranges, χ values to cells of the plurality of cells based on the cells determined flow characteristic values in comparison to the characteristic cutoff values; 
  selectively increasing the assigned χ value of at least one cell of the plurality of cells, the selectively increasing comprising increasing the assigned χ value of the at least one cell where the at least one cell shares a border with at least one seed cell of the plurality of cells, the at least one seed cell having the highest χ value ‘R’; and 
  identifying a viscous region of the at least one viscous region where multiple contiguous cells of the plurality of cells have χ values equal to or greater than a set χ value threshold; 
  evaluating the at least one viscous region by performing viscous domain solve for the at least one viscous region within the bounded domain; 
  providing a model of the bounded domain using, at least in part, results of the viscous domain solve; and 
 using the model in providing the data center layout optimized for energy efficiency of the data center, wherein the data center is configured based on the model. 
 
 
 
 
     
     
       2. The data center of  claim 1 , wherein the defining comprises defining three characteristic cutoff values (ω cutoff1 <ω cutoff2 <ω cutoff3 ) corresponding to three decreasing percentiles (P 1 >P 2 >P 3 ) of the flow characteristic value within the bounded domain, and wherein the assigning comprises for a cell i of the plurality of cells within the bounded domain, assigning a χ i  value based on the characteristic value (ω i ) for the cell i as follows: 
       
         
           
             
               
                 χ 
                 i 
               
               = 
               
                 { 
                 
                   
                     
                       
                         0 
                         , 
                       
                     
                     
                       
                         
                           ω 
                           i 
                         
                         < 
                         
                           ω 
                           
                             cutoff 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           1 
                           / 
                           4 
                         
                         , 
                       
                     
                     
                       
                         
                           ω 
                           
                             cutoff 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ≤ 
                         
                           ω 
                           i 
                         
                         < 
                         
                           ω 
                           
                             cutoff 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           1 
                           / 
                           2 
                         
                         , 
                       
                     
                     
                       
                         
                           ω 
                           
                             cutoff 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ≤ 
                         
                           ω 
                           i 
                         
                         < 
                         
                           ω 
                           
                             cutoff 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                     
                   
                   
                     
                       
                         R 
                         , 
                       
                     
                     
                       
                         
                           ω 
                           i 
                         
                         ≥ 
                         
                           ω 
                           
                             cutoff 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                         
                       
                     
                   
                 
               
             
           
         
         where:
 R=the set viscous region cell radius; 
 ω i =flow characteristic value for cell i; 
 ω cutoff1 =flow characteristic value at which P 1  of the cells have higher flow characteristic value; 
 ω cutoff2 =flow characteristic value at which P 2  of the cells have higher flow characteristic value; and 
 ω cutoff3 =flow characteristic value at which P 3  of the cells have higher flow characteristic value. 
 
       
     
     
       3. The data center of  claim 1 , wherein the selectively increasing further comprises expanding the viscous region by a growth function based on each cell's χ value, each cell's neighboring cells' χ values, and whether or not the cell is adjacent to a boundary of the bounded domain. 
     
     
       4. The data center of  claim 3 , wherein the selectively increasing comprises determining whether any cell at an inlet or outlet boundary of the bounded domain has a χ value ≥1, and if so, then all cells adjacent to that inlet or outlet boundary are assigned to have a χ value equal to the maximum of {1, χ i }. 
     
     
       5. The data center of  claim 3 , wherein the selectively increasing further comprises selectively increasing the assigned χ value of one or more cells to an assigned χ value equal to 1 where any of the following conditions are met: 
       
         
           
                 
                 
                 
                 
                 
               
                     
                 
                     
                     
                     
                   Minimum number of 
                   Cell is adjacent 
                 
                     
                   Condition 
                   χ i   
                   adjacent cells with χ = 1 
                   to a boundary 
                 
                     
                 
                     
                   1 
                   ½ 
                   1 
                   — 
                 
                     
                   2 
                   ¼ 
                   2 
                   — 
                 
                     
                   3 
                   ¼ 
                   1 
                   Yes 
                 
                     
                   4 
                   0 
                   3 
                   — 
                 
                     
                   5 
                   0 
                   2 
                    Yes. 
                 
                     
                 
             
                
                
                
                
               
               
                
                
                
                
                
                
               
            
           
         
       
     
     
       6. The data center of  claim 1 , wherein the selectively increasing comprises selectively increasing the assigned χ value of each cell of the at least one cell to the highest χ value ‘R’ of the adjacent seed cell minus 1. 
     
     
       7. The data center of  claim 1 , wherein the flow characteristic comprises vorticity magnitude and the determining comprises determining a vorticity magnitude value for each cell of the plurality of cells of the bounded domain. 
     
     
       8. The data center of  claim 1 , wherein the defining comprises defining three characteristic cutoff values (ω cutoff1 <ω cutoff2 <ω cutoff3 ) corresponding to three decreasing percentiles (P 1 >P 2 >P 3 ) of the flow characteristic value within the bounded domain. 
     
     
       9. The data center of  claim 1 , wherein the set χ value threshold equals 1, and the selectively increasing results in growing the viscous region of the at least one viscous region. 
     
     
       10. The data center of  claim 1 , wherein the selectively increasing comprises growing the viscous region outward from the at least one seed cell, the selectively increasing comprising recursively changing the χ value of any border cell i sharing a border with the at least one seed cell to the maximum of {R−1, χ i } and then processing any border cell as a seed-type cell by changing the χ value of any cell i sharing a border with that border cell to the maximum of {R−2, χ i }. 
     
     
       11. The data center of  claim 1 , further comprising, prior to the evaluating, comparing a ratio (η n ) of overall size of the at least one viscous region to overall size of the bounded domain against set minimum (η min ) and maximum (η max ) allowable ratios, and if the ratio (η n ) is less than the set minimum (η min ) or greater than the set maximum (η max ), then one or more of the defined characteristic cutoff values or the highest χ value ‘R’ are adjusted, and the assigning, selectively increasing and identifying are repeated. 
     
     
       12. The data center of  claim 1 , wherein:
 the processing of the bounded domain comprises processing the bounded domain to automatically locate and separate within the bounded domain the at least one viscous region and at least one inviscid region of the bounded domain; 
 the evaluating comprises separately evaluating the at least one viscous region and the at least one inviscid region by performing the viscous domain solve for the at least one viscous region within the bounded domain and inviscid domain solve for the at least one inviscid region within the bounded domain; and 
 the providing comprises providing the model of the bounded domain using the results of the viscous domain solve and the inviscid domain solve.